Can you solve it? From Russia with logic

Mathematicians get ready to party

UPDATE: The solutions can be read here.

The largest and most important event in the mathematical calendar will take place next July in St Petersburg. The International Congress of Mathematicians is a quadrennial gathering at which many of the subject's most prominent thinkers give lectures and the winners of maths' most prestigious prize, the Fields Medal, are announced.

As part of the build-up to the event - which is expected to attract about 5,000 mathematicians from all over the world - the organisers earlier this year ran an online maths competition for students and the general public. Below are the first three questions from this test.